The Janson inequalities for general up‐sets. Issue 2 (26th June 2013)

• Record Type: Journal Article
• Authors: Riordan, Oliver; Warnke, Lutz
• Is Part Of: Random structures & algorithms. Volume 46:Issue 2(2015)
• Page Start: 391
• Page End: 395
• Publication Date: 2013-06-26
• Subjects: Random graphs -- Periodicals; Mathematical analysis -- Periodicals; 519
• DOI: 10.1002/rsa.20506
• Languages: English
• ISSNs: 1042-9832

Abstract

<abstract abstract-type="main"> <title>Abstract</title> <p>Janson and Janson, Łuczak and Ruciński proved several inequalities for the lower tail of the distribution of the number of events that hold, when all the events are up‐sets (increasing events) of a special form—each event is the intersection of some subset of a single set of independent events (i.e., a principal up‐set). We show that these inequalities in fact hold for arbitrary up‐sets, by modifying existing proofs to use only positive correlation, avoiding the need to assume positive correlation conditioned on one of the events. © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 46, 391–395, 2015</p> </abstract>